It depends
The point of the Given/When/Then pattern is that it describes test preconditions (Given), actions (When), and expected results (Then) - very similar to the unit test arrange/act/assert pattern.
In the example you've given the actions are implied: the user navigates to the website. Depending on what's needed to prove the user's access, that could mean the user has already logged on, or it could mean the website lets everyone use it. There's nothing in your example to indicate either way, so a When statement could be helpful to clarify.
While I prefer to see the When statement so it's clear what has to be done to reach the Then condition, when it's the only action that can be taken to reach the Then condition, there may be no need to state it - if that's what the audience of the test prefers.
I'd write this test slightly differently:
Scenario: My website does not require special permissions or log on.
- Given I have an open web browser
- When I navigate to
mywebsite.mybogushost.org
- Then I see the full site
Your scenario could also be handled as:
- When I go to my website
- Then I see the full site
because there are no real preconditions.